XPS 15 Screen Goes Black and Laptop Freezes

I got an XPS 15 yesterday, Monday. Within 10 minutes of booting it the first time, before I had really done anything, I saw two glitches on the screen. A couple of minutes later the screen went black and the computer froze. Nothing would make it respond. I held down the power button to force a shutdown.

I installed the Dell updates and the latest Windows 10 updates, and the screen went black and the machine hung several times over the next few hours. It didn't seem to have anything to do with what I was doing -- it hung when I was in a browser, starting Windows update, and when the machine was idle with no apps running.

I installed the latest nVidia drivers. 

I turned off sleep in both Windows and the Intel HD Graphics control panel, thinking there might be a conflict with two different pieces of software trying to control sleeping. It didn't help.

I ran the diagnostics twice, both times with no errors detected.

I installed the current Intel HD graphics driver from the Dell website, and the latest WiFi driver.

The laptop did not hang when I expected it to: during intensive graphics card usage rendering frames in Blender. It performs very well doing this, so I'd really like to keep the machine.

The hanging continued today, with a couple of screen glitches. I chatted with Dell support in India, and they had two suggestions: reset the PC from scratch or send it back. I reset the PC. It reinstalled Windows and it restarted.

Within a couple minutes after logging into Windows for the first time the screen went black and the system was hung. I shut it down by holding down the power button. Then I rebooted.

That's where I am now. I'm ready to send the computer back and be rid of the thing unless someone has some idea how to fix this.